The text for geas says the following about removing the spell:

A remove curse, greater restoration, or wish spell also ends it.

However, you can already use wish to replicate remove curse or greater restoration and thus end geas. It seems redundant.

What's the difference if it didn't mention using Wish? Is there a genuine mechanical difference that I'm missing?

It is conceivable for a sorcerer to not know of a cleric spell to wish for in order to remove geas, per David Coffron’s answer. It’s a good point and I’ve upvoted that answer; it certainly is a difference.

But I find it isn’t a very compelling one. After all, not mentioning wish would take up less space, and thus save Wizards of the Coast money. I’ve worked in the RPG publishing business—publishers do not print things they don’t feel they have to print; it’s expensive. A corner-case like that doesn’t seem to justify the expense.

That difference may well be the only mechanical difference between the two approaches, but there are other differences between the two that should be considered—are more compelling, in my opinion, for answering the implicit question here—why this way and not the other way?

Player approachability

Players may not be familiar with wish when they get geas cast on them. They may not know that wish can copy remove curse or greater restoration. This is a far greater concern for Wizards of the Coast than the sorcerer not knowing about those spells—repetition is a big part of how human beings learn, and for many players, this may not even be a repeat. An accessible ruleset should be directing players to look into things that could be relevant to them when possible.

A continued tradition

Notably, this way is how D&D has traditionally handled wish—that is, wish has traditionally been listed as healing all manner of afflictions, even when those afflictions could be cured through spells wish was well capable of emulating. For example, the 3.5e version of bestow curse mentions wish alongside remove curse, which absolutely could have just been copied by wish. Longtime D&D players are used to wish being mentioned as a solution to all manner of afflictions. Failing to do so could give some of them to incorrect impression that something about wish has changed.

But most importantly, because wish is special

One might well point out that “the traditional approach” doesn’t really address the question but rather just shifts it—it wasn’t always the traditional approach, at some point someone first decided to do it this way. Player approachability might well have been the reason for doing so then, but there is another—more fundamental, and I would argue, important reason to mention wish explicitly when it could just be implied.

That is, a difference between mentioning wish explicitly and letting it be implied is that mentioning it explicitly mentions wish explicitly. This isn’t a means to an end—it is an end in and of itself. Mentioning wish explicitly all over the ruleset establishes, and reinforces, that wish is something special. In fact, “being special” is arguably wish’s raison d’etre.

Wish is special. Even among 9th-level spells, wish stands out. And that is because wish solves one critical problem. Sometimes that problem is not having the spell you need. But more often—both in game, and especially in narrative precedent—the purpose of a wish is to undo a dire malady. Think about it: when wishes come from a genie, power and wealth are common choices, but genies are special because they provide relatively casual access to the power of wishing. Otherwise, when wishes come true, they are usually the result of magic, the universe, divine forces, whatever, responding to some desperate plea—“save her!” “give him back!” and so on.

And that is why one of wish’s most important purviews is healing—because removing a deadly affliction, or death, is a huge part of what actually gets wished for. It establishes wish as the ultimate solution, the desperate last-ditch attempt to save someone. It comes at a cost, and at a risk, but it will get the job done.

So having afflictions list wish, over and over, even when it’s redundant to do so, as a valid solution, means that you keep seeing wish in these kinds of circumstances. It means readers can become familiar with the spell even if they never read it. They become aware that wish is out there, and that it is special.

The difference is the cost of wish

If a character doesn't know that greater restoration or remove curse will work, they may cast wish to try to ensure that the geas spell ends. In this instance it is an option of wish that is not to replicate a spell and is subject to this rule:

The stress of casting this spell to produce any effect other than duplicating another spell weakens you. After enduring that stress, each time you cast a spell until you finish a long rest, you take 1d10 necrotic damage per level of that spell. This damage can't be reduced or prevented in any way. In addition, your strength drops to 3, if it isn't 3 or lower already, for 2d4 days. For each of those days that you spend resting and doing nothing more than light activity, your remaining recovery time decreases by 2 days. Finally, there is a 33 percent chance that you are unable to cast wish ever again if you suffer this stress.

Primary reason might be because you can't normally cast the lower level spells

If you are playing in a world where there aren't spellcasting services readily available, then you are limited by the spells your party members can cast. The addition of Wish closes the loop so that the players know there is a workaround they might not have considered.

Greater Restoration can usually only be cast by Bards, Clerics, Druids and Celestial Warlocks

Remove Curse can usually only be cast by Clerics, Paladins, Warlocks, and Wizards

Wish can usually only be cast by Sorcerers and Wizards

If Wish wasn't a choice and you had a sorcerer and no other caster type you wouldn't have a method of removal.

Metagaming prevention?

If you don't have someone who can cast Greater Restoration or Remove Curse, they can still cast Wish to either replicate that particular spell or use Wish alone (and possibly suffer the penalties for doing so) if they don't actually know that either of the other spells would work.